Encyclopedia of Espionage, Intelligence, and Security

Enigma

█ LARRY GILMAN

Enigma was a ciphering (code communication) system used by the German
military from 1926 until the end of World War II, and by several other
nations for some years after. Enigma was the first mechanized
message-encryption system to see wide use. Enigma produced such thoroughly
scrambled messages that for many years its cipher was considered
unbreakable both by the German military and its foes. Polish and British
mathematicians, however, cracked the Enigma cipher in time to give the
Allies access to most German military communications throughout World War
II. The German government never knew that the Enigma cipher had been
broken and that its military communications were often transparent, giving
a significant advantage to the Allies on many occasions. The Japanese
military also used a cipher related to Enigma during World War II. The
Japanese version of Enigma was cracked by American cryptographers,
providing a crucial advantage to the Allies in the Pacific theater. U.S.
knowledge of secrete Japanese transmissions was essential, for example, to
victory at the crucial battle at Midway, the Japanese navy's first
major defeat in several centuries. Many military strategists and
historians hold that Allied success in cracking the Enigma and related
ciphers helped significantly shorten World War II.

Origin of Enigma.
During World War I, cumbersome paper-and-pencil ciphers were still the
rule, as they had been for centuries past. (A
cipher
is any scheme for transforming ordinary written language—
plaintext
—into a coded, but apparently random string of characters,
ciphertext
.) After World War I, several inventors turned their attention to the
mechanization of ciphering, seeking to increase accuracy, speed, and
security. The most successful of these inventors was German engineer
Arthur Scherbius, who in 1918, created a cipher machine he named the
Enigma. (This is not a translation; the word "enigma" is the
same in German and English). Scherbius was unsuccessful in selling Enigma
to commercial buyers. It was not until 1923 that Enigma was chosen by the
German government as its standard ciphering system, as Germany had only
just learned how much damage had been done by the breaking of its ciphers
by the Allies in World War I. Between 1925 and 1945, the German military
bought over 30,000 Enigma machines, deploying slightly different systems
to its European armies, its army in North Africa, its air force, and its
navy.

The Enigma cipher.
The Enigma cipher is built upon the simplest of all cipher types, the
substitution cipher. In a substitution cipher, one letter of the alphabet
is substituted directly for another. A substitution cipher for a sixletter
alphabet might appear as:

Plaintext: A B C D E F
Ciphertext: F C A B D E

Using this cipher, the plaintext word BAD (for example) would produce the
ciphertext word CFB. Such ciphers are easy to implement, but also contain
easily broken code, as their ciphertext contains all the regularities of

A four-rotor Enigma machine, right, which was used by the crews of
German U-boats in World War II to send coded messages.

AP/WIDE WORLD PHOTOS

.

ordinary language: that is, double letters in plaintext appear as double
letters in ciphertext, the ciphertext letter for "e" will
appear in the ciphertext just as often as "e" appears in
plaintext, and so forth. Such codes are weak because analyzing
regularities is one of the primary means by which codebreakers attack
codes.

However, by adding complications to this simple idea, a powerful code can
be devised. Consider the following substitution cipher for a three-letter
alphabet:

Plaintext: A B C
Ciphertext: A C B

In this simple example, A is enciphered as itself. This cipher can be
imagined as a physical device consisting of three disks or dials arranged
in a row. The first (left-hand) and third (right-hand) disks, each of
which has the alphabet ABC spaced evenly around its edge, are identical,
and are aligned so that their letters are in the same positions; the third
disk, which sandwiched between the other two, is different. It contains
three wires that pass from its left side right through to its right,
connecting the two alphabet disks so that the A of the left-hand disk is
wired to the A of the right-hand disk, the B of the left-hand disk to the
C of the right-hand disk, and the C of the left-hand disk to the B of the
right-hand disk. In effect, the middle disk scrambles the alphabet. The
result is a simple substitution cipher. If the middle disk, (the
scrambler) is rotated, however, so that the wire which touched A on the
plaintext disk now touches C on that disk, all the other letters on the
plaintext and ciphertext disks will also be connected differently by the
scrambler, producing the following substitution cipher:

Plaintext: A B C
Ciphertext: B A C

This can be verified by describing the wires in the scrambler as a set of
input-output rules, one for each wire:

Connect input position 1 to output position 1.

Connect input position 2 to output position 3.

Connect input position 3 to output position 2.

By rule 1, when scrambler input position 1 is lined up with the letter A
on the left-hand (plaintext) disk, it is connected to output position 1,
which is lined up with the
letter A on the right-hand (ciphertext) disk. The other two substitutions
are produced by the other two wires: B → C, C → B. When the
scrambler is rotated so that its input 1 moves from A to C on the
plaintext disk, its output 1 moves from A to C on the ciphertext disk.
Now, instead of producing A → A, wire 1 produces C → C. The
other two wires now produce the substitutions A → B, B → A.
Thus, each time the scrambler is rotated by one letter position, a new
different substitution code is produced. This continues until the
scrambler returns to its starting position, whereupon the substitution
codes produced by the device begin to repeat. In this example, repetition
begins with the third shift of the scrambler.

Rotation of the scrambler can be used to make a cipher that is more
formidable than a straightforward substitution. Consider a three-letter
plaintext message is to be sent: ABA. First, A is enciphered with the
scrambler in the first position described above: A → A. Before the
second letter is encrypted, the scrambler disk is rotated by one
letter-position. The second plaintext letter is then enciphered: B
→ A. The disk is rotated, and A is enciphered again: A → C.
Although in this case one would start repeating substitutions after only
three letters, the resulting cipher is significantly more complex, and
thus harder to crack, than a static substitution cipher.

Decryption in this system is simple as long as the receiving party
possesses an identical machine; the wires in the scrambler disk work
equally well in either direction, so decryption is simply encryption run
backwards. The receiver must, however, begin decrypting with their
scrambler set to the same position as the sender's at the start of
transmission, otherwise the substitution codes used by the receiver to
decipher the message will be out of step with those used by the sender to
encipher it, and decipherment will fail.

The Enigma system was based upon the scramblerdisk principle described
above. Enigma used not a 3-letter, but a 26-character alphabet and not
one, but four scrambler disks. The first scrambler scrambled plaintext or
ciphertext, the second scrambler scrambled the outputs of the first
scrambler, the third scrambled the outputs of the second, and the fourth
fed back, or "reflected," the outputs of the third so that
messages passed through the other three scramblers before the encrypted
ciphertext (or decrypted plaintext) was read. Each letter was thus
scrambled a total of seven times during its passage through the machine.
Three of the scrambler disks could be rotated freely, but the fourth, the
"reflector," was stationary.

In order to use an Enigma unit, its operator typed plaintext or ciphertext
into a keyboard. For each keystroke typed, Enigma automatically shifted
one or more of its scramblers and lit up a letter on a display board. The
letter on the display board showed the output text for the typed input
letter: ciphertext if plaintext was input, plaintext if ciphertext was
input. To produce further scrambling between ciphertext and plaintext,
each Enigma also had a built-in commutator or "plugboard"
that enabled the operator to crisscross paired letters of the alphabet
before their signals fed into the first scrambler disk. The result was
that Enigma had over 10
20
different "keys" or distinct settings of scramblers and
plugboard. Simply guessing the correct key for a given message was,
therefore, essentially impossible. Every day at midnight, all operators of
a given Enigma system would switch to a new key; these initial daily keys
were printed in a codebook that was distributed to the operators. For
added security, the scrambler-disks part of the key was changed for every
single message sent; this message-key information was transmitted twice at
the beginning of every message. This technique was intended to prevent
message loss due to transmission errors, but in fact reduced
Enigma's effectiveness by introducing an element of predictability.

The defeat of Enigma.
Enigma was long considered impossible to crack. However, in 1931, a
disgruntled German exofficer gave drawings for the machine to the French
secret service. The French, who considered Enigma too tough to crack even
with this information in their possession, gave it to the Polish
government. Polish mathematician Marian Rejewski (1905–1980) used
it to devise automatic devices (specialized electromechanical calculators)
for re-cracking the ever-changing Enigma cipher on a daily basis. Just
before the fall of Poland in 1939, Rejewski's findings were
transferred to the British government, which continued to improve them.

During World War II, the German military modified the Enigma system at
intervals, requiring the British to continue re-cracking the cipher
throughout the war. With the help of a motley team of crossword-puzzle
experts, bridge devotees, chess champions, mathematicians, and linguists
led by British mathematician and computing pioneer Alan Turing
(1912–1954), the group succeeded. Tragically, however, Turing was
persecuted after the war for his homosexuality. His security clearance was
revoked, he was forced to undergo debilitating hormone treatments, and he
was banned from the development of the digital computer. Turing committed
suicide in 1954, some 20 years before his crucial contribution to the
cracking of Enigma, and thus, to the Allied victory, was declassified.